Modulation and multiple access technique using orbital angular momentum

ABSTRACT

The present invention as disclosed and described herein, in one aspect thereof, comprises a method for multiple access communications over a communications link involves receiving a plurality of data streams from a plurality of data sources. The plurality of data streams are grouped into a plurality of groups. Orthogonal frequency division multiplexing (OFDM) processing is applied to each of the plurality of groups. Each of the plurality of groups uses a same combination of frequency and time slot combinations in the OFDM processing. A different orthogonal function is applied to each of the OFDM processed groups to uniquely identify each of the OFDM processed group from each other and the orthogonal function processed groups are transmitted over the communications link.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of U.S. Provisional Application No.62/035,217, filed Aug. 8, 2014, entitled NEW MODULATION AND MULTIPLEACCESS TECHNIQUE USING ORBITAL ANGULAR MOMENTUM (Atty. Dkt. No.NXGN-32315), the specification of which is incorporated herein byreference in its entirety.

TECHNICAL FIELD

The present invention relates to multiple axis processing techniques,and more particularly to utilizing orbital angular momentum processingin parallel with orthogonal frequency division multiplexing in order toincrease channel bandwidth within a data transmission system.

BACKGROUND

The use of voice and data networks has greatly increased as the numberof personal computing and communication devices, such as laptopcomputers, mobile telephones, Smartphones, tablets, et cetera, hasgrown. The astronomically increasing number of personal mobilecommunication devices has concurrently increased the amount of databeing transmitted over the networks providing infrastructure for thesemobile communication devices. As these mobile communication devicesbecome more ubiquitous in business and personal lifestyles, theabilities of these networks to support all of the new users and userdevices has been strained. Thus, a major concern of networkinfrastructure providers is the ability to increase their bandwidth inorder to support the greater load of voice and data communications andparticularly video that are occurring. Traditional manners forincreasing the bandwidth in such systems have involved increasing thenumber of channels so that a greater number of communications may betransmitted, or increasing the speed at which information is transmittedover existing channels in order to provide greater throughput levelsover the existing channel resources.

However, while each of these techniques have improved system bandwidths,existing technologies have taken the speed of communications to a levelsuch that drastic additional speed increases are not possible, eventhough bandwidth requirements due to increased usage are continuing togrow exponentially. Additionally, the number of channels assigned forvoice and data communications, while increasing somewhat, have notincreased to a level to completely support the increasing demands of avoice and data intensive use society. Thus, there is a great need forsome manner for increasing the bandwidth throughput within existingvoice and data communication that increases the bandwidth on existingvoice and data channels.

Another issue arising in communication systems is limited channelbandwidth providing only a set number of communication channels whichmay be established between a transmitting and receiving unit. Theincreased use of voice and data communications has created an increasedneed for greater channel availability in order to provide connectionsfor a growing number of customers.

SUMMARY

A method for multiple access communications over a communications linkinvolves receiving a plurality of data streams from a plurality of datasources. The plurality of data streams are grouped into a plurality ofgroups. Orthogonal frequency division multiplexing (OFDM) processing isapplied to each of the plurality of groups. Each of the plurality ofgroups uses a same combination of frequency and time slot combinationsin the OFDM processing. A different orthogonal function is applied toeach of the OFDM processed groups to uniquely identify each of the OFDMprocessed group from each other and the orthogonal function processedgroups are transmitted over the communications link.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding, reference is now made to thefollowing description taken in conjunction with the accompanyingDrawings in which:

FIG. 1 is a functional block diagram of a system for generating orbitalangular momentum within a communication system;

FIG. 2 is a functional block diagram of the orbital angular momentumsignal processing block of FIG. 1;

FIG. 3 is a functional block diagram illustrating the manner forremoving orbital angular momentum from a received signal including aplurality of data streams;

FIG. 4 illustrates a single wavelength having two quanti-spinpolarizations providing an infinite number of signals having variousorbital angular momentums associated therewith;

FIG. 5A illustrates an object with only a spin angular momentum;

FIG. 5B illustrates an object with an orbital angular momentum;

FIG. 5C illustrates a circularly polarized beam carrying spin angularmomentum;

FIG. 5D illustrates the phase structure of a light beam carrying anorbital angular momentum;

FIG. 6A illustrates a plane wave having only variations in the spinangular momentum;

FIG. 6B illustrates a signal having both spin and orbital angularmomentum applied thereto;

FIGS. 7A-7C illustrate various signals having different orbital angularmomentum applied thereto;

FIG. 7D illustrates a propagation of Poynting vectors for various Eigenmodes;

FIG. 7E illustrates a spiral phase plate;

FIG. 8 illustrates an example of a Poincare sphere;

FIGS. 9A-9C illustrate examples of simple trajectories on Poincarespheres that can be implemented as a modulation process;

FIG. 10 illustrates a representation of an OFDM signal;

FIG. 11 illustrates an OFDM system model for generating an OFDM signal;

FIG. 12 illustrates a receiver circuit;

FIG. 13 illustrates the manner in which an inverse fast Fouriertransform converts a plurality of modulated signals into a single signalstream;

FIG. 14 illustrates the structure of OFDM carrier symbols;

FIG. 15 illustrates a generic frame structure for E-UTRA, FDD and TDDmodes;

FIG. 16 illustrates a downlink resource grid structure;

FIG. 17 illustrates a manner for assigning resource blocks to users inan OFDM system;

FIG. 18 illustrates the use of OAM or other orthogonal functions toincrease OFDM bandwidth;

FIG. 19 illustrates a block diagram of a system for processing datastreams using an OFDM format;

FIG. 20 illustrates a block diagram of an OFDM receiver;

FIG. 21 illustrates a flow diagram describing the operation of thetransmitter and receiver of FIGS. 19 and 20;

FIG. 22A illustrates a quarterwave plate;

FIG. 22B illustrates a halfwave plate;

FIG. 22C illustrates a Poincare sphere;

FIG. 23 illustrates a Wigner transform;

FIG. 24 illustrates changes in spin;

FIG. 25 illustrates change in orbital angular momentum; and

FIG. 26 illustrates concentric Poincare spheres each associated with adifferent orbital angular momentum.

DETAILED DESCRIPTION

Referring now to the drawings, wherein like reference numbers are usedherein to designate like elements throughout, the various views andembodiments of new modulation and multiple access technique usingorbital angular momentum are illustrated and described, and otherpossible embodiments are described. The figures are not necessarilydrawn to scale, and in some instances the drawings have been exaggeratedand/or simplified in places for illustrative purposes only. One ofordinary skill in the art will appreciate the many possible applicationsand variations based on the following examples of possible embodiments.

Referring now more particularly to FIG. 1, there is illustrated afunctional block diagram of a system for generating the orbital angularmomentum “twist” within a communication system, such as that illustratedwith respect to FIG. 3, to provide a data stream that may be combinedwith multiple other data streams for transmission upon a same wavelengthor frequency. Multiple data streams 102 are provided to the transmissionprocessing circuitry 100. Each of the data streams 102 comprises, forexample, an end to end connection carrying a voice call or a packetconnection transmitting non-circuit switch packed data over a dataconnection. The multiple data streams 102 are processed bymodulator/demodulator circuitry 104. The modulator/demodulator circuitry104 modulates the received data stream 102 onto a wavelength orfrequency channel using a multiple level overlay modulation technique,as will be more fully described herein below. The communications linkmay comprise an optical fiber link, free-space optics link, RF microwavelink, RF satellite link, wired link (without the twist), etc.

The modulated data stream is provided to the orbital angular momentum(OAM) signal processing block 106. Each of the modulated data streamsfrom the modulator/demodulator 104 are provided a different orbitalangular momentum by the orbital angular momentum electromagnetic block106 such that each of the modulated data streams have a unique anddifferent orbital angular momentum associated therewith. Each of themodulated signals having an associated orbital angular momentum areprovided to an optical transmitter 108 that transmits each of themodulated data streams having a unique orbital angular momentum on asame wavelength. Each wavelength has a selected number of bandwidthslots B and may have its data transmission capability increase by afactor of the number of degrees of orbital angular momentum l that areprovided from the OAM electromagnetic block 106. The optical transmitter108 transmitting signals at a single wavelength could transmit B groupsof information. The optical transmitter 108 and OAM electromagneticblock 106 may transmit l×B groups of information according to theconfiguration described herein.

In a receiving mode, the optical transmitter 108 will have a wavelengthincluding multiple signals transmitted therein having different orbitalangular momentum signals embedded therein. The optical transmitter 108forwards these signals to the OAM signal processing block 106, whichseparates each of the signals having different orbital angular momentumand provides the separated signals to the demodulator circuitry 104. Thedemodulation process extracts the data streams 102 from the modulatedsignals and provides it at the receiving end using the multiple layeroverlay demodulation technique.

Referring now to FIG. 2, there is provided a more detailed functionaldescription of the OAM signal processing block 106. Each of the inputdata streams are provided to OAM circuitry 202. Each of the OAMcircuitry 202 provides a different orbital angular momentum to thereceived data stream. The different orbital angular momentums areachieved by applying different currents for the generation of thesignals that are being transmitted to create a particular orbitalangular momentum associated therewith. The orbital angular momentumprovided by each of the OAM circuitries 202 are unique to the datastream that is provided thereto. An infinite number of orbital angularmomentums may be applied to different input data streams using manydifferent currents. Each of the separately generated data streams areprovided to a signal combiner 204, which combines the signals onto awavelength for transmission from the transmitter 206.

Referring now to FIG. 3, there is illustrated an embodiment in which theOAM processing circuitry 106 may separate a received signal intomultiple data streams. The receiver 302 receives the combined OAMsignals on a single wavelength and provides this information to a signalseparator 304. The signal separator 304 separates each of the signalshaving different orbital angular momentums from the received wavelengthand provides the separated signals to OAM de-twisting circuitry 306. TheOAM de-twisting circuitry 306 removes the associated OAM twist from eachof the associated signals and provides the received modulated datastream for further processing. The signal separator 304 separates eachof the received signals that have had the orbital angular momentumremoved therefrom into individual received signals. The individuallyreceived signals are provided to the receiver 302 for demodulationusing, for example, multiple level overlay demodulation as will be morefully described herein below.

FIG. 4 illustrates in a manner in which a single wavelength orfrequency, having two quanti-spin polarizations may provide an infinitenumber of twists having various orbital angular momentums associatedtherewith. The l axis represents the various quantized orbital angularmomentum states which may be applied to a particular signal at aselected frequency or wavelength. The symbol omega (ω) represents thevarious frequencies to which the signals of differing orbital angularmomentum may be applied. The top grid 402 represents the potentiallyavailable signals for a left handed signal polarization, while thebottom grid 404 is for potentially available signals having right handedpolarization.

By applying different orbital angular momentum states to a signal at aparticular frequency or wavelength, a potentially infinite number ofstates may be provided at the frequency or wavelength. Thus, the stateat the frequency Δω or wavelength 406 in both the left handedpolarization plane 402 and the right handed polarization plane 404 canprovide an infinite number of signals at different orbital angularmomentum states Δl. Blocks 408 and 410 represent a particular signalhaving an orbital angular momentum Δl at a frequency Δω or wavelength inboth the right handed polarization plane 404 and left handedpolarization plane 410, respectively. By changing to a different orbitalangular momentum within the same frequency Δω or wavelength 406,different signals may also be transmitted. Each angular momentum statecorresponds to a different determined current level for transmissionfrom the optical transmitter. By estimating the equivalent current forgenerating a particular orbital angular momentum within the opticaldomain and applying this current for transmission of the signals, thetransmission of the signal may be achieved at a desired orbital angularmomentum state.

Thus, the illustration of FIG. 4, illustrates two possible angularmomentums, the spin angular momentum, and the orbital angular momentum.The spin version is manifested within the polarizations of macroscopicelectromagnetism, and has only left and right hand polarizations due toup and down spin directions. However, the orbital angular momentumindicates an infinite number of states that are quantized. The paths aremore than two and can theoretically be infinite through the quantizedorbital angular momentum levels.

It is well-known that the concept of linear momentum is usuallyassociated with objects moving in a straight line. The object could alsocarry angular momentum if it has a rotational motion, such as spinning(i.e., spin angular momentum (SAM) 502), or orbiting around an axis 506(i.e., OAM 504), as shown in FIGS. 5A and 5B, respectively. A light beammay also have rotational motion as it propagates. In paraxialapproximation, a light beam carries SAM 502 if the electrical fieldrotates along the beam axis 506 (i.e., circularly polarized light 505),and carries OAM 504 if the wave vector spirals around the beam axis 506,leading to a helical phase front 508, as shown in FIGS. 5C and 5D. Inits analytical expression, this helical phase front 508 is usuallyrelated to a phase term of exp(ilθ) in the transverse plane, where θrefers to the angular coordinate, and l is an integer indicating thenumber of intertwined helices (i.e., the number of 2π phase shifts alongthe circle around the beam axis). l could be a positive, negativeinteger or zero, corresponding to clockwise, counterclockwise phasehelices or a Gaussian beam with no helix, respectively.

Two important concepts relating to OAM include:

1) OAM and polarization: As mentioned above, an OAM beam is manifestedas a beam with a helical phase front and therefore a twistingwavevector, while polarization states can only be connected to SAM 502.A light beam carries SAM 502 of ±h/2π (h is Plank's constant) per photonif it is left or right circularly polarized, and carries no SAM 502 ifit is linearly polarized. Although the SAM 502 and OAM 504 of light canbe coupled to each other under certain scenarios, they can be clearlydistinguished for a paraxial light beam. Therefore, with the paraxialassumption, OAM 504 and polarization can be considered as twoindependent properties of light.

2) OAM beam and Laguerre-Gaussian (LG) beam: In general, an OAM-carryingbeam could refer to any helically phased light beam, irrespective of itsradial distribution (although sometimes OAM could also be carried by anon-helically phased beam). LG beam is a special subset among allOAM-carrying beams, due to that the analytical expression of LG beamsare eigen-solutions of paraxial form of the wave equation in acylindrical coordinates. For an LG beam, both azimuthal and radialwavefront distributions are well defined, and are indicated by two indexnumbers, l and p, of which l has the same meaning as that of a generalOAM beam, and p refers to the radial nodes in the intensitydistribution. Mathematical expressions of LG beams form an orthogonaland complete basis in the spatial domain. In contrast, a general OAMbeam actually comprises a group of LG beams (each with the same l indexbut a different p index) due to the absence of radial definition. Theterm of “OAM beam” refers to all helically phased beams, and is used todistinguish from LG beams.

Using the orbital angular momentum state of the transmitted energysignals, physical information can be embedded within the radiationtransmitted by the signals. The Maxwell-Heaviside equations can berepresented as:

$\begin{matrix}{{{\nabla{\cdot E}} = \frac{\rho}{ɛ_{0}}}{{\nabla{\times E}} = {- \frac{\partial B}{\partial t}}}{{\nabla{\cdot B}} = 0}{\nabla{\times B}} = {{ɛ_{0}\mu_{0}\frac{\partial E}{\partial t}} + {\mu_{0}{j( {t,x} )}}}} & (2)\end{matrix}$

where ∇ is the del operator, E is the electric field intensity and B isthe magnetic flux density. Using these equations, one can derive 23symmetries/conserved quantities from Maxwell's original equations.However, there are only ten well-known conserved quantities and only afew of these are commercially used. Historically if Maxwell's equationswhere kept in their original quaternion forms, it would have been easierto see the symmetries/conserved quantities, but when they were modifiedto their present vectorial form by Heaviside, it became more difficultto see such inherent symmetries in Maxwell's equations.

The conserved quantities and the electromagnetic field can berepresented according to the conservation of system energy and theconservation of system linear momentum. Time symmetry, i.e. theconservation of system energy can be represented using Poynting'stheorem according to the equations:

$H = {{\sum\limits_{i}^{\;}\; {m_{i}\gamma_{i}c^{2}}} + {\frac{ɛ_{0}}{2}{\int{{^{3}{x( {{E}^{2} + {c^{2}{B}^{2}}} )}}\mspace{14mu} {Hamiltonian}\mspace{14mu} ( {{total}\mspace{14mu} {energy}} )}}}}$$\mspace{20mu} {{\frac{U^{mech}}{t} + \frac{U^{em}}{t} + {{\oint_{s^{\prime}}}^{\;}\ {{^{2}x^{\prime}}{{\hat{n}}^{\prime} \cdot S}}}} = {0\mspace{14mu} {conservation}\mspace{14mu} {of}\mspace{14mu} {energy}}}$

The space symmetry, i.e., the conservation of system linear momentumrepresenting the electromagnetic Doppler shift can be represented by theequations:

$\mspace{20mu} {p = {{\sum\limits_{i}^{\;}\; {m_{i}\gamma_{i}v_{i}}} + {ɛ_{0}{\int{{^{3}x}( {E \times B} )\mspace{14mu} {linear}\mspace{14mu} {momentum}}}}}}$${\frac{p^{mech}}{t} + \frac{p^{em}}{t} + {\oint_{s^{\prime}}\mspace{7mu} {{^{2}x^{\prime}}{{\hat{n}}^{\prime} \cdot T}}}} = {0\mspace{14mu} {conservation}\mspace{14mu} {of}\mspace{14mu} {linear}\mspace{14mu} {momentum}}$

The conservation of system center of energy is represented by theequation:

$\begin{matrix}{R = {{\frac{1}{H}{\sum\limits_{i}^{\;}\; {( {x_{i} - x_{0}} )m_{i}\gamma_{i}c^{2}}}} + {\frac{ɛ_{0}}{2H}{\int\; {{^{3}{x( {x - x_{0}} )}}( {{E^{2}} + {c^{2}{B^{2}}}} )}}}}} & (3)\end{matrix}$

Similarly, the conservation of system angular momentum, which gives riseto the azimuthal Doppler shift is represented by the equation:

${\frac{J^{mech}}{t} + \frac{J^{em}}{t} + {\oint_{s^{\prime}}{{^{2}x^{\prime}}{{\hat{n}}^{\prime} \cdot M}}}} = {0\mspace{14mu} {conservation}\mspace{14mu} {of}\mspace{14mu} {angular}\mspace{14mu} {momentum}}$

For radiation beams in free space, the EM field angular momentum J^(em)can be separated into two parts:

J ^(em)=∫_(v′) d ³ x′(E×A)+ε₀∫_(v′) d ³ x′E _(i)[(x′−x ₀)×∇]A _(i)

For each singular Fourier mode in real valued representation:

$\begin{matrix}{J^{em} = {{{- }\frac{ɛ_{0}}{2\omega}{\int_{V^{\prime}}^{\;}\mspace{7mu} {^{3}{x^{\prime}( {E^{*} \times E} )}}}} - {\frac{ɛ_{0}}{2\; \omega}{\int_{V^{\prime}}^{\;}\mspace{7mu} {{^{3}x^{\prime}}{E_{i}\lbrack {( {x^{\prime} - x_{0}} ) \times \nabla} \rbrack}E_{i}}}}}} & (5)\end{matrix}$

The first part is the EM spin angular momentum S^(em), its classicalmanifestation is wave polarization. And the second part is the EMorbital angular momentum L^(em) its classical manifestation is wavehelicity. In general, both EM linear momentum P^(em), and EM angularmomentum J^(em)=L^(em)+S^(em) are radiated all the way to the far field.

By using Poynting theorem, the optical vorticity of the signals may bedetermined according to the optical velocity equation:

$\begin{matrix}{{{\frac{\partial U}{\partial t} + {\nabla{\cdot S}}} = 0},} & {{continuity}\mspace{14mu} {equation}}\end{matrix}$

where S is the Poynting vector

S=¼(E×H*+E*×H),   (6)

and U is the energy density

U=¼(ε|E| ²+μ₀ |H| ²),   (7)

with E and H comprising the electric field and the magnetic field,respectively, and ε and μ₀ being the permittivity and the permeabilityof the medium, respectively. The optical vorticity V may then bedetermined by the curl of the optical velocity according to theequation:

$\begin{matrix}{V = {{\nabla{\times v_{opt}}} = {\nabla{\times ( \frac{{E \times H^{*}} + {E^{*} \times H}}{{ɛ{E}^{2}} + {\mu_{0}{H}^{2}}} )}}}} & (8)\end{matrix}$

Referring now to FIGS. 6A and 6B, there is illustrated the manner inwhich a signal and its associated Poynting vector in a plane wavesituation. In the plane wave situation illustrated generally at 602, thetransmitted signal may take one of three configurations. When theelectric field vectors are in the same direction, a linear signal isprovided, as illustrated generally at 604. Within a circularpolarization 606, the electric field vectors rotate with the samemagnitude. Within the elliptical polarization 608, the electric fieldvectors rotate but have differing magnitudes. The Poynting vectorremains in a constant direction for the signal configuration to FIG. 6Aand always perpendicular to the electric and magnetic fields. Referringnow to FIG. 6B, when a unique orbital angular momentum is applied to asignal as described here and above, the Poynting vector S 610 willspiral about the direction of propagation of the signal. This spiral maybe varied in order to enable signals to be transmitted on the samefrequency as described herein.

FIGS. 7A-7C illustrate the differences in signals having differenthelicity (i.e., orbital angular momentums). Each of the spiralingPoynting vectors associated with the signals 602, 604, and 606 provide adifferent shaped signal. Signal702 has an orbital angular momentum of+1, signal 704 has an orbital angular momentum of +3, and signal 706 hasan orbital angular momentum of −4. Each signal has a distinct angularmomentum and associated Poynting vector enabling the signal to bedistinguished from other signals within a same frequency. This allowsdiffering type of information to be combined on the same frequency,since these signals are separately detectable and do not interfere witheach other (Eigen channels).

FIG. 7D illustrates the propagation of Poynting vectors for variousEigen modes. Each of the rings 720 represents a different Eigen mode ortwist representing a different orbital angular momentum within the samefrequency. Each of these rings 720 represents a different orthogonalchannel. Each of the Eigen modes has a Poynting vector 722 associatedtherewith.

Topological charge may be multiplexed to the frequency for either linearor circular polarization. In case of linear polarizations, topologicalcharge would be multiplexed on vertical and horizontal polarization. Incase of circular polarization, topological charge would multiplex onleft hand and right hand circular polarizations. The topological chargeis another name for the helicity index “I” or the amount of twist or OAMapplied to the signal. The helicity index may be positive or negative.In RF, different topological charges can be created and muxed togetherand de-muxed to separate the topological charges.

The topological charges l s can be created using Spiral Phase Plates(SPPs) as shown in FIG. 6E using a proper material with specific indexof refraction and ability to machine shop or phase mask, hologramscreated of new materials or a new technique to create an RF version ofSpatial Light Modulator (SLM) that does the twist of the RF waves (asopposed to optical beams) by adjusting voltages on the device resultingin twisting of the RF waves with a specific topological charge. SpiralPhase plates can transform a RF plane wave (l=0) to a twisted RF wave ofa specific helicity (i.e. l=+1).

These embodiments can create cross talk and multipath interference.However, cross talk and multipath interference can be corrected using RFMultiple-Input-Multiple-Output (MIMO). In one embodiment, most of thechannel impairments can be detected using a control or pilot channel andbe corrected using algorithmic techniques (closed loop control system).However, other techniques can be used to eliminate these channelimpairments.

Cross talk and multipath interference can be corrected using RFMultiple-Input-Multiple-Output (MIMO). Most of the channel impairmentscan be detected using a control or pilot channel and be corrected usingalgorithmic techniques (closed loop control system).

While the application of orbital angular momentum to various signalsallow the signals to be orthogonal to each other and used on a samesignal carrying medium, other orthogonal function/signals can be appliedto data streams to create the orthogonal signals on the same signalmedia carrier.

Within the notational two-dimensional space, minimization of the timebandwidth product, i.e., the area occupied by a signal in that space,enables denser packing, and thus, the use of more signals, with higherresulting information-carrying capacity, within an allocated channel.Given the frequency channel delta (Δf), a given signal transmittedthrough it in minimum time Δt will have an envelope described by certaintime-bandwidth minimizing signals. The time-bandwidth products for thesesignals take the form;

Δt Δf=½(2n+1)

where n is an integer ranging from 0 to infinity, denoting the order ofthe signal.

These signals form an orthogonal set of infinite elements, where eachhas a finite amount of energy. They are finite in both the time domainand the frequency domain, and can be detected from a mix of othersignals and noise through correlation, for example, by match filtering.Unlike other wavelets, these orthogonal signals have similar time andfrequency forms. These types of orthogonal signals that reduce the timebandwidth product and thereby increase the spectral efficiency of thechannel.

Hermite-Gaussian polynomials are one example of a classical orthogonalpolynomial sequence, which are the Eigenstates of a quantum harmonicoscillator. Signals based on Hermite-Gaussian polynomials possess theminimal time-bandwidth product property described above, and may be usedfor embodiments of MLO systems. However, it should be understood thatother signals may also be used, for example orthogonal polynomials suchas Jacobi polynomials Gegenbauer polynomials, Legendre polynomials,Chebyshev polynomials, and Laguerre-Gaussian polynomials. Q-functionsare another class of functions that can be employed as a basis for MLOsignals.

In addition to the time bandwidth minimization described above, theplurality of data streams can be processed to provide minimization ofthe Space-Momentum products in spatial modulation. In this case:

ΔxΔp=½

Processing of the data streams in this manner create wavefronts that arespatial. The above described scheme is applicable to twisted pair,coaxial cable, fiber optic, RF satellite, RF broadcast, RF point-topoint, RF point-to-multipoint, RF point-to-point (backhaul), RFpoint-to-point (fronthaul to provide higher throughput CPRI interfacefor cloudification and virtualization of RAN and cloudified HetNet),free-space optics (FSO), Internet of Things (IOT), Wifi, Bluetooth, as apersonal device cable replacement, RF and FSO hybrid system, Radar,electromagnetic tags and all types of wireless access. The method andsystem are compatible with many current and future multiple accesssystems, including EV-DO, UMB, WIMAX, WCDMA (with or without),multimedia broadcast multicast service (MBMS)/multiple input multipleoutput (MIMO), HSPA evolution, and LTE.

Multiple Access Techniques Using Orbital Angular Momentum

Multiple access techniques improve the overall spectral efficiency of anorthogonal frequency division multiplexing (OFDM) system at the physicallayer. OFDM is used within Wi-Fi, WiMAX and LTE systems. Electromagneticwaves carry a spin angular momentum (a quantum feature) that ismanifested to polarization states (a classic feature). However,electromagnetic waves can carry an orbital angular momentum (a quantumfeature) or other orthogonal states that is manifested to helicity andphase structure (a classic feature). This orbital angular momentum isindependent of the polarization state and therefore independent of spin.Within a La-Guerre Gaussian mode having an azimuthal phase term, orbitalangular momentum eigentstates can carry an orbital angular momentumvalue.

Photon polarization provides a useful physical realization of a qubitand is employed in demonstrations of quantum key distribution. However,measurements of the polarization only provide one bit of information bya photon. However, waves carrying orbital angular momentum (OAM) canpotentially have many helicities or other orthogonal states and aretherefore not limited to only two states of a positive or negative spin.

The polarization states can be completely characterized in terms of theStokes parameter or visualized on a Poincare sphere. A Stokes parameteris a value describing the polarization state of a wave. Consequently,the Stokes parameters are the Cartesian coordinates of a space in whichany completely polarized beam is represented by a point on a Poincaresphere with a unit radius around the origin. An example of a Poincaresphere is illustrated in FIG. 8. Within a Poincare sphere 802, any stateof polarization can be uniquely represented by a point on or within theunit sphere 802 centered on a rectangular coordinate system. Thecoordinates of the point are the three normalized Stokes parametersdescribing the state of polarization. The degree of polarizationcorresponds to a point that is a distance of that point from thecoordinate origin, and can vary from zero at the origin (unpolarized) tounity at the surface of the sphere (completely polarized). Linearpolarizations are located at the equator 804. Examples of this are shownat points 806. Circular polarizations are located at the pole of thePoincare sphere 802 at points 808. Intermediate elliptical polarizationsare continuously distributed at locations between the equators 804 andthe pole 808.

Because a state of polarization is represented by a point, a continuousevolution of polarization can be represented as a continuous path on thePoincare sphere 802. For example, the evolution of polarization forlight traveling through a waveplate or birefringent crystal can berepresented by a circular arc about an axis drawn through two pointsrepresenting the eigenmodes at the medium. Eigenmodes are polarizationsthat propagate unchanged through the medium. The real, three-dimensionalspace of the Poincare surface is closely linked to the complextwo-dimensional space of Jones vectors. Most physical ideas can beexpressed in either context and mathematically linked to angularmomentums.

A new modulation scheme using orbital angular momentum or otherorthogonal states of the waves are used as a degree of freedom toperform modulation. The modulation can be traced as a trajectory on thesurface of a Poincare sphere. If this path is known only between atransmitter and a receiver, this can be a method for both securecommunication as well as modulation techniques using polarization asopposed to amplitude, frequency or phase. The transmitter would use themodulation represented by the trajectory on the Poincare sphere tomodulate and transmit data while the receiver would use the trajectoryto demodulate data at the receiver. Referring now to FIGS. 9A-9C, thereare provided some examples of simple trajectories that can beimplemented as a modulation process. However, any complicated path canbe implemented on the surface of the eigensphere.

As referenced previously, the polarization states of a monochromaticlight beam can be characterized by Stokes parameters as follows:

$P_{1} = \frac{I_{0{^\circ}} - I_{90{^\circ}}}{I_{0{^\circ}} + I_{90{^\circ}}}$$P_{2} = \frac{I_{45{^\circ}} - I_{135{^\circ}}}{I_{45{^\circ}} + I_{135{^\circ}}}$$P_{3} = \frac{I_{R} - I_{L}}{I_{R} + I_{L}}$

I is the intensities recorded through various orientations of linearpolarizer's and I_(R) and I_(L) are the intensities of the circularlypolarized components in the beam. The polarization states may be addedtogether such that P₁ ²+P₂ ²+P₃ ²=1. This means that the polarized beamcan be represented by a point on a sphere with a unit radius, i.e. aPoincare sphere. Any point on the Poincare sphere can be described as asuperposition of left and right-handed circular polarizations. Thus, alinearly polarized beam is a superposition of equal intensities of I_(R)and I_(L).

An analogous sphere can be constructed for superposition of left andright-handed Laguerre Gaussian modes with azimuthal phase term e^(±ilφ)which are OAM Eigen states (LG₀ ^(+l), LG₀ ^(−l)) and have orbitalangular momentum of +l½ and −l½ per photon.

Therefore, in an analogous manner to Stoke's parameters, a set ofparameters with respect to Hermite Gaussian modes may be represented as:

$0_{1} = \frac{I_{{HG}_{1,0}^{0{^\circ}}} - I_{{HG}_{1,0}^{90{^\circ}}}}{I_{{HG}_{1,0}^{0{^\circ}}} + I_{{HG}_{1,0}^{90{^\circ}}}}$$0_{2} = \frac{I_{{HG}_{1,0}^{45{^\circ}}} - I_{{HG}_{1,0}^{135{^\circ}}}}{I_{{HG}_{1,0}^{45{^\circ}}} + I_{{HG}_{1,0}^{135{^\circ}}}}$$0_{3} = \frac{I_{{LG}_{0}^{1}} - I_{{LG}_{0}^{- 1}}}{I_{{LG}_{0}^{1}} + I_{{LG}_{0}^{- 1}}}$0₁² + 0₂² + 0₃² = 1

As shown in FIG. 22A, I_(L) applied to a quarter wave plate 4502provides an output of either I₄₅ or I_(R). For implementation of such amodulation technique the quarter wave plate 4502 can be used to convertintensity of left hand polarization beams to linear intensity of 45degrees. An application of a second quarter wave plate 2204 can thenconvert the linear intensity at 45 degrees to an intensity of right handpolarization. Thus, a half wave plate can convert a left handpolarization intensity to a right hand polarization intensity as shownin FIG. 22B covering a trajectory from the north of the Poincare sphereto it its equator and further south of the Poincare sphere as shown inFIG. 22C. The relative phase of 2 HG modes (m=1, n=0) at 90 degrees toeach other can be controlled by an arrangement of cylindrical lensesthat leverage changes in relative Gouy phase to transform HG modes intoLG modes and vice versa. A Wigner transform can mathematically modelthis transformation as shown in FIGS. 23 and 24. Changes in orbitalangular momentum can similarly transform as shown in FIG. 25.

The Poincare sphere provides a geometrical representation ofpolarization on the surface of the sphere. The Poincare representationis closely connected to the SU(2) structure of the transformations ofthe polarization states of an electromagnetic field which can describestates of orbital angular momentum (OAM) where both Laguerre-Gaussian(LG) and Hermite Gaussian (HG) can be represented on this sphere.Therefore modulation using LG and/or HG can be thought of as atrajectory on this new sphere and other concentric spheres for differentorders of LG/HG as shown in FIG. 48. Thus, the states of orbital angularmomentum with an underlying SU(2) structure on the same sphere for bothclassical and quantum fields. In analogy to the coherence matrix, we canintroduce a matrix that partially describes coherent beams with orbitalangular momentum. Thus, as illustrated in FIG. 26, a path for modulatingusing orbital angular momentum may be represented by a series of spheres2602 that are concentric with respect to each other. The path ratherthan traveling over the surface of a single sphere passes between thesurfaces of the multiple spheres 2602. Knowing this path signals may bemodulated and then demodulated between a transmitter to a receiver in asimilar manner as described herein above with respect to a path on thesurface of a single sphere rather than between the surfaces of multiplespheres.

Starting from Maxwell's equations in free space, one can derive the waveequations that describe the electric field. From this wave equation, onecan perform a paraxial approximation and arrived the paraxial waveequation. Maxwell's equations and the EM wave equations are representedby:

Maxwell's Equations and EM Wave Equations Maxwell's Equations

Gauss^(′)  Laws ∇⋅D = ρ ∇⋅B = 0 Faraday’s  Law${\nabla{\times E}} = {- \frac{\partial B}{\partial t}}$Ampere’s  Law${\nabla{\times H}} = {J + \frac{\partial D}{\partial t}}$∇²E + k²E = 0 (Full  Wave  Equation)

Wave Equations

${\frac{^{2}E}{x^{2}} + \frac{^{2}E}{y^{2}} + \frac{^{2}E}{z^{2}} + {k^{2}E}} = 0$(Rectangular)${{\frac{1}{\rho}\frac{\;}{\rho}( {\rho \frac{\;}{\rho}} )E} + {\frac{1}{\rho^{2}}\frac{^{2}}{\phi^{2}}E} + \frac{^{2}E}{z^{2}} + {k^{2}E}} = 0$(Cylindrical)

The wave equations may then be converted to a paraxial wave equation inthe following manner:

Paraxial Approximation Full Wave Equations

${\frac{^{2}E}{x^{2}} + \frac{^{2}E}{y^{2}} + \frac{^{2}E}{z^{2}} + {k^{2}E}} = 0$(Rectangular)${{\frac{1}{\rho}\frac{\;}{\rho}( {\rho \frac{\;}{\rho}} )E} + {\frac{1}{\rho^{2}}\frac{^{2}\;}{\phi^{2}}E} + \frac{^{2}E}{z^{2}} + {k^{2}E}} = 0$(Cylindrical) $\frac{E}{t}\operatorname{>>}\frac{^{2}E}{t^{2}}$

Paraxial Wave Equations

${\frac{^{2}E}{x^{2}} + \frac{^{2}E}{y^{2}} + \frac{2{jk}{E}}{z}} = 0$(Rectangular)${{\frac{1}{\rho}\frac{\;}{\rho}( {\rho \frac{\;}{\rho}} )E} + {\frac{1}{\rho^{2}}\frac{^{2}\;}{\phi^{2}}E} + \frac{2j\; k{E}}{z}} = 0$(Cylindrical)

Finally the practical wave equation may be used to determine a HermiteGaussian equation as follows for the rectangular solution:

Paraxial Wave Equation:

${\frac{^{2}E}{x^{2}} + \frac{^{2}E}{y^{2}} + \frac{2j\; k{E}}{z}} = 0$

Solution: Hermite-Gaussian (HG):

${\frac{^{2}E}{x^{2}} + \frac{^{2}E}{y^{2}} + \frac{2j\; k{E}}{z}} = 0$

Or from the paraxial equation to a Laguerre Gaussian equation for thecylindrical solution:

Paraxial Wave Equation

${\frac{^{2}E}{x^{2}} + \frac{^{2}E}{y^{2}} + \frac{2j\; k{E}}{z}} = 0$

Solution: Laguerre-Gaussian (LG)

${E( {\rho,\phi,z} )} = {\sum\limits_{}\; {\sum\limits_{p}\; {C_{\; p}E_{0}{\frac{w_{0}}{w(z)}\lbrack \frac{\sqrt{2}\rho}{w(z)} \rbrack}^{}{L_{}^{p}\lbrack \frac{\sqrt{2}\rho}{w(z)} \rbrack}^{\frac{- \rho^{2}}{w^{2}{(z)}}}^{{- {j{({{2p} +  + 1})}}}\tan^{- 1}\frac{z}{z_{0}}}^{j\phi}^{\frac{j\; {k{(\rho^{2})}}}{2{R{(z)}}}}}}}$

For LG beam:

E = (ℰ₊b₊ + ℰ⁻b⁻)f ^(−j wt), where  f  is  the  normalization  factorb_(±) = strength  of  LG₀^(±e)[b₊, b₊⁺] = 1[b⁻, b⁻⁺] = 1[b₊, b⁻⁺] = 0${E_{\pm}( {x,y} )} = {\mathcal{E}_{0}^{{\pm j}\; \theta}r\; ^{\frac{- r^{2}}{w^{2}}}}$

For HG beam:

E = (ℰ₁b₁ + ℰ₂b₂)f ^(−j w t)$\mathcal{E}_{\pm} = {{\frac{\mathcal{E}_{1} \pm {j\mathcal{E}}_{2}}{\sqrt{2}}\lbrack {b_{\alpha},b_{\beta}^{+}} \rbrack} = \delta_{\alpha\beta}}$$b_{1} = \frac{b_{+} + b_{-}}{\sqrt{2}}$$b_{2} = \frac{j( {b_{+} - b_{-}} )}{\sqrt{2}}$$b_{\pm} = \frac{b_{1} + {j\; b_{2}}}{\sqrt{2}}$

SU(2) Structure:

Schwinger-Boson representation for angular momentum operators:

-   -   conservation of photon # N    -   s² constant

s⁺ = b₊ + b⁻ s⁻ = b⁻ + b₊$s^{z} = {\frac{1}{2}( {b_{+} + b_{+} - b_{-} + b_{-}} )}$$s^{2} = {\frac{N^{2}}{4} + \frac{N}{2}}$ N = (b₊ + b₊ + b⁻ + b⁻)

It is possible to create commutation relations for LG beam as well as HGbeams and further expand the SU(2) structure with the Schwinger-Bosonrepresentation for angular momentum operators.

The downlink transmission scheme for E-UTRA (evolved universalterrestrial radio access), frequency division duplex (FDD) mode and timedivision duplex (TDD) mode is based on conventional OFDM. Referring nowto FIG. 10, within an OFDM system, the available spectrum is dividedinto multiple carriers, called sub-carriers 1002, which are orthogonalto each other. Each of these sub-carriers 302 is independently modulatedby a low rate data stream. OFDM is used as well in WLAN (Wireless LocalArea Network), WiMAX (Worldwide Interoperability for Microwave Access)and broadcast technologies like DVB (Digital Video Broadcasting). OFDMhas several benefits including its robustness against multipath fadingand its efficient receiver architecture. FIG. 10 illustrates arepresentation of an OFDM signal 1000. A signal 1000 with a 4 MHzbandwidth 1004 is shown. The principle is, of course, the same for otherE-UTRA bandwidths. Data symbols are independently modulated andtransmitted over a high number of closely spaced orthogonal sub-carriers1002. In E-UTRA, downlink modulation schemes such as QPSK, 16QAM and64QAM are available. In the time domain, a guard interval 1006 may beadded to each symbol 1008 to combat inter-OFDM-symbol-interference dueto channel delay spread. In E-UTRA, the guard interval 1006 is a cyclicprefix which is inserted prior to the OFDM symbol 1008.

Referring now to FIG. 11, there is illustrated an OFDM system model forgenerating an OFDM signal. An OFDM carrier signal 1102 is the sum of anumber of orthogonal subcarriers, with baseband data on each sub-carrierbeing independently modulated using some type of quadrature amplitudemodulation (QAM) or phase-shift keying (PSK). This is a compositebaseband signal typically used to modulate a main RF carrier. Signals[n] 1104 is a serial stream of binary digits. A serial to parallelconverter 1106 uses inverse multiplexing to demultiplex the serialstream into N parallel streams. Each of the N parallel streams aremapped to a symbol stream using a modulator 1108 applying, for example,quadrature amplitude modulation, PSK modulation, etc. The modulators1108 may utilize different modulation schemes so that some streams maycarry a higher data rate than others. The modulated data streams x_(n)are applied to an inverse fast Fourier transform 1110. The inverse fastFourier transform 1110 is computed for each set of symbols, giving a setof complex time-domain samples that are output as a real portion 1112and an imaginary portion 1114. The samples are quadrature-mixed topassband in the standard manner. The real component 1112 and imaginarycomponent 1114 are converted to analog signals via digital-to-analogconverter 1116. The analog signal output from the digital-to-analogconverter 1116 are modulated within a mixing circuit 1118. The analogsignals are used to modulate cosine and sine waves at the carrierfrequency f_(c) 1120. The carrier signal 1120 is applied directly to themixing circuit 1118 of the real signals and is offset by 90 degrees at1122 before being applied to the mixing circuit 1118 of the imaginaryanalog signals. The mixed signals are summed at a summing circuit 1124to give the transmission signal s_(t) 1102.

Referring now also to FIG. 12, there is illustrated the receivercircuit. The receiver picks up the received signal r(t) 1202. Thereceived signal 1202 is quadrature-mixed down to baseband using sine andcosine waves at mixer 1204 with the carrier frequency 1206. The basebandsignals are applied to samplers 1208 and the real and imaginary portionsare digitized using analog-to-digital converters 1210. The digitizedreal and imaginary signals are applied to a fast Fourier transform 1212to convert the signals back into the frequency domain. The frequencysignals Y_(N) are converted into a binary stream using an appropriatesymbol detector 1214. The detected streams are recombined into a serialstream s[n] 1216 through a parallel-to-serial convertor 1218. The signals[n] 1216 comprises an estimate of the original binary stream at thetransmitter (FIG. 11).

Referring now to FIG. 13, there is illustrated the manner in which theinverse fast Fourier transform 1110 receives the plurality of modulatedsignals from the modulators 1108 and converts these into a single signalstream 1304.

FIG. 14 more generally illustrates the structure of the OFDM carriersymbols. The various data sources 1402 provide the data streams to a QAMmodulator 1404 for modulation of the source signals. The QAM modulatedsignals are applied to the serial-to-parallel convertor 1406 thatconverts the serial data streams into a number of N symbol streams thatare applied to the inverse fast Fourier transform 410. The generatedOFDM signals are combined into a single OFDM signal stream inparallel-to-serial convertor 1406.

In contrast to an OFDM transmission scheme, OFDMA (orthogonal frequencydivision multiplexing access) allows the access of multiple users on theavailable bandwidth. Each user is assigned a specific time-frequencyresource. As a fundamental principle of a E-UTRA system, the datachannels are shared channels, i.e., for each transmission time intervalof 1 ms, a new scheduling decision is taken regarding which users areassigned to which time/frequency resources during a transmission timeinterval. Referring now to FIG. 15, a generic frame structure is definedfor both E-UTRA, FDD and TDD modes. Additionally, an alternative framestructure is defined for a TDD mode only. For the generic framestructure, the 10 ms radio frame 1502 is divided into 20 equally sizedslots 1504 of 0.5 ms. A sub-frame 1506 consists of two consecutive slotssuch that one radio frame consists of 10 sub-frames. Within FIG. 15,T_(s) is expressing the basic time unit corresponding to 30.72 MHz. OFDMradio frames contain a frame period of 10 ms, one subframe and two timeslots within each time slot of period of ½ ms in the time domain. Thesubcarriers in the frequency domain are separated by 15khz with 12subcarriers creating a resource block. The frame structure can bethought of as a plane in time frequency of order of zero helicity (FIG.17). However other planes in an orthogonal direction to time andfrequency can be structured that would include positive helicity as wellas negative helicity. While the mode division multiplexing modulation(MDM) using orthogonal LG and/or HG are applicable to OFDM frame, thetechnique is applicable to any OFDM based multiple access system (WiFi,y-max, LTE, 5G, 4G, 3G, ect.). It is possible to perform modulationbased on polarization states as well as MDM states or combined states.

Referring now to FIG. 16, there is illustrated the structure of adownlink resource grid for the duration of one downlink slot 1602. Theavailable downlink bandwidth consists of _(DL)N_(BW) sub-carriers 1604with a spacing of f=15 kHz. In the case of multi-cell MBMS (multimediabroadcast multicast service) transmission, a subcarrier spacing of f=7.5kHz is also possible. _(DL)N_(BW) can vary in order to allow forscalable bandwidth operations up to 20 MHz. Initially, the bandwidthsfor LTE were explicitly defined within the layer 1 specification. Lateron, a bandwidth agnostic layer 1 was introduced, with _(DL)N_(BW) forthe different bandwidths to be specified by 3GPP RAN4 to meetperformance requirements, e.g., for out-of-band transmissionrequirements and regulatory emission limits. Each of the subcarriersincludes a number of resource elements 1606. Each resource element 1606is associated with their particular subcarrier 1604 and an OFDM symbol1608.

Referring now to FIG. 17, there is provided an illustration of themanner in which a scheduler may assign various resource blocks (i.e,channels) to users within an OFDM system. The resource blocks 1702 areeach designated via a frequency on the frequency axis 1704 and a time onthe time axis 1706. The total number of resource blocks available to thescheduler is limited by the available frequency bandwidth 1708 and theavailable time slots 1710. The bandwidth 1708 can only include a limitednumber of sub-frequencies 1712. The scheduler algorithm controlling thescheduler block can be configured to operate in three dimensions oftime, frequency and OAM states to select the best resource block forcommunication such that multiple time and frequency planes would beavailable for selection with each plane associated with a different OAMstate (FIG. 18).

Referring now also to FIG. 18, there is illustrated the manner in whichthe use of orbital angular momentum or other orthogonal functions may beused to provide increased OFDM bandwidth by applying differing orbitalangular momentums or other orthogonal functions to each resource grid1802. This new multiple access technique utilizes the various OAM orother orthogonal function states as a new degree of freedom within thecontext of the OFDM frame structure. This technique can use six positivetwisted states l=+1, +2, +3, +4, +5, +6 and six negative twisted statesl=−1, −2, −3, −4, −5, −6 for a total of 12 twisted states similar toeach subcarrier. These states 1804 are totally orthogonal states andtherefore can be used as a new orthogonal axis within the time-frequencyspace. The scheduler can now use different resource block from any ofthese states. Thus, the frequency-time combination at l=+1 can also beused for l=+2, l=−2, l=−3 and so forth. Thus, the scheduler isalgorithmically three-dimensional. This multiple access technique isreferenced as OLDM (where L stand for the usual symbol l used torepresent quantized orbital angular momentum states or helicity of thewaves). MDM states (LG/HG) can be used for modulation (as indicated on aPoincare Sphere) and/or as a multiple access technology with a new framestructure.

Referring now to FIG. 19, there is provided a generalize block diagramof the manner in which a series of data streams 1902 may be processed toprovide transmission of information using the OFDM format. Variousgroups of data streams 1902 are provided to OFDM processing circuitries1904. Each of the OFDM processing circuitries 1904 process the datastreams 1902 to generate an OFDM output of data assigned to particularchannels within the various resource blocks as illustrated in FIG. 10.Each of the outputs of the OFDM circuitry 1904 will have data assignedto a same resource block defined by a particular subcarrier and timeslot. Each of the OFDM process data streams are applied to OAM (or otherorthogonal) processing circuitry 1906. The OAM (or other orthogonal)processing circuitry 1906 applies a different orbital angular momentumor other orthogonal function to each of the resource grids coming froman individual OFDM circuitry 1904. Thus, it adds the third dimension ofprocessing to the equation with each of the resource slots beingrepresented by a frequency, time and a particular orbital angularmomentum or other orthogonal function value. This OLDM processed outputis provide to an optical/RF transmitter 1908 which may transmit theinformation over an RF or optical link 1910.

Referring now to FIG. 20, a transmitted signal is received over an RF oroptical link 1210 at an optical or RF receiver 2002. The OFDM signal isoutput by the receiver 2002 to OAM processing circuitry 2004 in order toderive the signal into each of the individual OFDM resource grids thatare associated with separate orbital angular momentum or otherorthogonal function values. The orbital angular momentum twist or otherorthogonal function value is removed and the remaining time andfrequency based signals are provided to an associated OFDM processingcircuitry 2006. The OFDM processing circuitry 2006 extracts each of theindividual channels associate with the various subcarriers and timeslots to provide multiple output data stream 2008.

Referring now to FIG. 21, there is provided a flow diagram moreparticularly describing the operation of the transmitter and receiver ofFIGS. 19 and 20. Initially, a plurality of data streams 2102 arereceived by the various OFDM processing circuitries 1904. The OFDMprocessing circuitries 1904 apply OFDM processing to each of the groupsof data streams at step 2104. Each OFDM processing circuitry 1904 willapply a same OFDM processing schemes such that data is assigned to sametime slots within an existing frequency/time grid structure. Next, eachof the channels associated with the frequency/time-grid structuresoutput from the OFDM circuitries 1904 are processed within the OAM orother orthogonal function processing circuitry 1906 to apply differentorbital angular momentums to each of the OFDM process data stream gridsat step 2106. The OLDM processed data is transmitted at step 2108 froman associated transmitter 1908. The data is received by a receiver 2002at step 2110. The OAM processing circuitry 2004 within the receiverremoves the orbital angular momentums applied to each of the receiveddata stream groups at step 2112 and decodes each of the data streamgroups using OFDM processing at step 2114. The recovered data streamsare output at step 2116.

As can be seen, the available bandwidth may be greatly increased byadding the third dimension of orbital angular momentum twists to theOFDM resource grid structure. In this manner, the number of OFDM gridscan be increased in the positive and negative direction by applicationof an associated orbital angular momentum.

It will be appreciated by those skilled in the art having the benefit ofthis disclosure that this new modulation and multiple access techniqueusing orbital angular momentum provides a greater bandwidth to an OFDMprocessing scheme. It should be understood that the drawings anddetailed description herein are to be regarded in an illustrative ratherthan a restrictive manner, and are not intended to be limiting to theparticular forms and examples disclosed. On the contrary, included areany further modifications, changes, rearrangements, substitutions,alternatives, design choices, and embodiments apparent to those ofordinary skill in the art, without departing from the spirit and scopehereof, as defined by the following claims. Thus, it is intended thatthe following claims be interpreted to embrace all such furthermodifications, changes, rearrangements, substitutions, alternatives,design choices, and embodiments.

What is claimed is:
 1. A method for multiple access communications overa communications link comprising: receiving a plurality of data streamsfrom a plurality of data sources; grouping the plurality of data streamsinto a plurality of groups; applying orthogonal frequency divisionmultiplexing (OFDM) processing to each of the plurality of groups,wherein each of the plurality of groups re-uses a combination offrequency and time slot combinations in the OFDM processing; applying adifferent orthogonal function to each of the OFDM processed groups touniquely identify each of the OFDM processed group from each other; andtransmitting orthogonal function processed groups over thecommunications link.
 2. The method of claim 1 further comprising:receiving the OAM processed groups over the communications link;removing the orbital angular momentum applied to each of the OFDMprocessed groups; separating the plurality of OFDM processed groups intothe separate OFDM processed groups; removing the OFDM processing fromeach of the OFDM processed groups to provide the plurality of datastreams; and outputting the plurality of data streams.
 3. The method ofclaim 1, wherein the step of transmitting further comprises transmittingthe OAM processed groups over an RF communications link.
 4. The methodof claim 1, wherein the step of transmitting further comprisestransmitting the OAM processed groups over an optical communicationslink.
 5. The method of claim 1, wherein the step of applying orthogonalfrequency division multiplexing (OFDM) processing further comprises thestep of generating a plurality of grids of channel slots, each grid ofthe plurality of grids defining a plurality of channel slots, each ofthe channel slots identified by an associated time and frequency.
 6. Themethod of claim 1, wherein the step of applying a different orbitalangular momentum (OAM) further comprises applying a different orbitalangular momentum to each of the plurality of grids.
 7. The method ofclaim 6, wherein the orbital angular momentum values vary from +3 to -3for each of the plurality of grids.
 8. The method of claim 1, whereinthe orthogonal function comprises an orbital angular momentum (OAM). 9.A system for providing multiple access communications over acommunications link, comprising: an interface for receiving a pluralityof data streams from a plurality of data sources; a multiplexor forgrouping the plurality of data streams into a plurality of groups; aplurality of orthogonal frequency division multiplexing (OFDM)processing circuitries for applying a same OFDM processing to each ofthe plurality of groups, wherein each of the plurality of OFDMprocessing circuitries uses a same combination of frequency and timeslot combinations on each of the plurality of groups; orbital angularmomentum processing circuitry for applying an orthogonal function toeach of the OFDM processed groups to uniquely identify each of the OFDMprocessed group from each other; and a transmitter transmittingorthogonal function processed groups over the communications link. 10.The system of claim 9 further comprising: a receiver for receiving theOAM processed groups over the communications link; a second orbitalangular momentum processing circuitry for removing the orbital angularmomentum applied to each of the OFDM processed groups; a secondmultiplexor for separating the plurality of OFDM processed groups intothe separate OFDM processed groups; and a second plurality of OFDMprocessing circuitries for removing the OFDM processing from each of theOFDM processed groups to provide the plurality of data streams.
 11. Thesystem of claim 9, wherein the transmitter further transmits the OAMprocessed groups over an RF communications link.
 12. The system of claim8, wherein the transmitter further transmits the OAM processed groupsover an optical communications link.
 13. The system of claim 9, whereinthe orthogonal frequency division multiplexing (OFDM) processingcircuitry further generates a plurality of grids of channel slots, eachgrid of the plurality of grids defining a plurality of channel slots,each of the channel slots identified by an associated time andfrequency.
 14. The system of claim 13, wherein the orbital angularmomentum processing circuitry applies a different orbital angularmomentum to each of the plurality of grids.
 15. The system of claim 14,wherein the orbital angular momentum values vary from +3 to −3 for eachof the plurality of grids.
 16. The system of claim 9, wherein the signalprocessing circuitry applies a different orbital angular momentum toeach of the OFDM processed groups.
 17. A method for multiple accesscommunications over a communications link comprising: receiving aplurality of data streams from a plurality of data sources; grouping theplurality of data streams into a plurality of groups; applyingorthogonal frequency division multiplexing (OFDM) processing to each ofthe plurality of groups, wherein each of the plurality of groups uses asame combination of frequency and time slot combinations in the OFDMprocessing; applying a different orbital angular momentum (OAM) to eachof the OFDM processed groups to uniquely identify each of the OFDMprocessed group from each other; transmitting OAM processed groups overthe communications link; receiving the OAM processed groups over thecommunications link; removing the orbital angular momentum applied toeach of the OFDM processed groups; separating the plurality of OFDMprocessed groups into the separate OFDM processed groups; and removingthe OFDM processing from each of the OFDM processed groups to providethe plurality of data streams.
 18. The method of claim 17, wherein thestep of transmitting further comprises transmitting the OAM processedgroups over an RF communications link.
 19. The method of claim 17,wherein the step of transmitting further comprises transmitting the OAMprocessed groups over an optical communications link.
 20. The method ofclaim 17, wherein the step of applying orthogonal frequency divisionmultiplexing (OFDM) processing further comprises the step of generatinga plurality of grids of channel slots, each grid of the plurality ofgrids defining a plurality of channel slots, each of the channel slotsidentified by an associated time and frequency.
 21. The method of claim17, wherein the step of applying a different orbital angular momentum(OAM) further comprises applying a different orbital angular momentum toeach of the plurality of grids.
 22. The method of claim 21, wherein theorbital angular momentum values vary from +3 to −3 for each of theplurality of grids.
 23. A method for multiple access communications overa communications link comprising: receiving orbital angular momentum(OAM) processed groups over the communications link; removing an orbitalangular momentum applied to each of a plurality of orthogonal frequencydivision multiplexed (OFDM) processed groups; separating the pluralityof OFDM processed groups into the separate OFDM processed groups;removing the OFDM processing from each of the OFDM processed groups toprovide the plurality of data streams; and outputting the plurality ofdata streams.
 24. The method of claim 23 further comprising: receivingthe plurality of data streams from a plurality of data sources; groupingthe plurality of data streams into a plurality of groups; applying theorthogonal frequency division multiplexing (OFDM) processing to each ofthe plurality of groups, wherein each of the plurality of groups re-usesa combination of frequency and time slot combinations in the OFDMprocessing; applying a different orbital angular momentum (OAM) to eachof the OFDM processed groups to uniquely identify each of the OFDMprocessed group from each other; and transmitting the OAM processedgroups over the communications link.
 25. The method of claim 23, whereinthe step of receiving further comprises receiving the OAM processedgroups over an RF communications link.
 26. The method of claim 23,wherein the step of receiving further comprises receiving the OAMprocessed groups over an optical communications link.
 27. The method ofclaim 24, wherein the step of applying orthogonal frequency divisionmultiplexing (OFDM) processing further comprises the step of generatinga plurality of grids of channel slots, each grid of the plurality ofgrids defining a plurality of channel slots, each of the channel slotsidentified by an associated time and frequency.
 28. The method of claim23, wherein the step of removing a different orbital angular momentum(OAM) further comprising removing a different orbital angular momentumfrom each of the plurality of grids having OFDM processing appliedthereto.
 29. The method of claim 28, wherein the orbital angularmomentum values vary from +3 to −3 for each of the plurality of grids.